// Source : https://leetcode-cn.com/problems/smallest-subtree-with-all-the-deepest-nodes/
// Author : jkbs487
// Date   : 2020-12-16

/***************************************************************************************************** 
 *
 * Given the root of a binary tree, the depth of each node is the shortest distance to the root.
 * 
 * Return the smallest subtree such that it contains all the deepest nodes in the original tree.
 * 
 * A node is called the deepest if it has the largest depth possible among any node in the entire tree.
 * 
 * The subtree of a node is tree consisting of that node, plus the set of all descendants of that node.
 * 
 * Note: This question is the same as 1123: 
 * https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/
 * 
 * Example 1:
 * 
 * Input: root = [3,5,1,6,2,0,8,null,null,7,4]
 * Output: [2,7,4]
 * Explanation: We return the node with value 2, colored in yellow in the diagram.
 * The nodes coloured in blue are the deepest nodes of the tree.
 * Notice that nodes 5, 3 and 2 contain the deepest nodes in the tree but node 2 is the smallest 
 * subtree among them, so we return it.
 * 
 * Example 2:
 * 
 * Input: root = [1]
 * Output: [1]
 * Explanation: The root is the deepest node in the tree.
 * 
 * Example 3:
 * 
 * Input: root = [0,1,3,null,2]
 * Output: [2]
 * Explanation: The deepest node in the tree is 2, the valid subtrees are the subtrees of nodes 2, 1 
 * and 0 but the subtree of node 2 is the smallest.
 * 
 * Constraints:
 * 
 * 	The number of nodes in the tree will be in the range [1, 500].
 * 	0 <= Node.val <= 500
 * 	The values of the nodes in the tree are unique.
 ******************************************************************************************************/


